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VOL. 9 | 2013 Consistent scoring functions for quantiles
Kyrill Grant, Tilmann Gneiting

Editor(s) M. Banerjee, F. Bunea, J. Huang, V. Koltchinskii, M. H. Maathuis

## Abstract

A scoring function is consistent for the $\alpha$-quantile functional if, and only if, it is generalized piecewise linear (GPL) of order $\alpha$, up to equivalence. Expressed differently, loss functions that yield quantiles as Bayes rules are GPL functions. We review and discuss this basic decision-theoretic result with focus on Thomson’s pioneering characterization.

## Information

Published: 1 January 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1327.62035
MathSciNet: MR3202632

Digital Object Identifier: 10.1214/12-IMSCOLL912

Subjects:
Primary: 62C05
Secondary: 91B06

Keywords: Bayes rule , consistent scoring function , fractile , optimal point forecast , proper scoring rule , quantile